Method and apparatus utilizing the phase velocity difference of light rays for measuring the velocity of a moving object

ABSTRACT

Light transmitted through an optical birefringent retardation plate emerges as ordinary (O) and extraordinary (E) rays having a phase velocity difference characteristic of the plate material and thickness. Retardation plate motion introduces an additional phase velocity difference between the E- and O-rays that is a measure of the velocity of such motion. Velocity of a moving object is measured by affixing an optical retardation plate to the moving object, detecting the E- and O-ray phase velocity difference of coherent light transmitted through the moving plate, and converting the phase velocity difference values so obtained to linear and angular velocity values.

United States Patent [1 1 Newburg [54] METHOD AND APPARATUS UTILIZING THE PHASE VELOCITY DIFFERENCE OF LIGHT RAYS FOR MEASURING THE VELOCITY OF A MOVING OBJECT [75] Inventor: Ronald G; Newburg, Belmont, Mass.

[73] Assignee: The United States of America as represented by the Secretary of the Air Force, Washington, DC.

[22] Filed: Apr. 28, 1972 [21] Appl. No.: 248,585

[5 6] References Cited UNITED STATES PATENTS 3,692,385 Gievers 350/147 PMAR/AID'ER [111 3,791,736 [451 Feb. 12, 1974 3,506,362 4/1970 Doyle et al. 356/106 LR Primary Examiner-Ronald L. Wibert Assistant ExaminerV. P. McGraw 5 7 ABSTRACT Light transmitted through an optical birefringent retardation plate emerges as ordinary (O) and extraordinary (E) rays having a phase velocity difference char acteristic of the plate material and thickness. Retardation plate motion introduces an additional phase velocity difference between the E- and O-rays that is a measure of the velocity of such motion. Velocity of a moving object is measured by affixing an optical retardation plate to the moving object, detecting the E- and O-ray phase velocity difference of coherent light transmitted through the moving plate, and converting the phase velocity difference values soobtained to linear and angular velocity values.

4 Claims, 2 Drawing Figures BACKGROUND OF THE INVENTION This invention relates to velocity measurement methods and devices, and in particular to means for remotely measuring and monitoring the linear and angular velocities of moving objects. It also finds utility as a laboratory device for testing the laws of composition of phase velocities. I

There are many applications in which the velocity of a moving object must be measured accurately. Often the requirement is to measure and monitor the velocity of an object moving in a hazardous environment. Such applications generally require both extremely accurate measurements and the capability of taking such measurements from a remote location. Currently available velocity measuring devices such as speedometers, tachometers, stroboscopes, electronic .devices, and radar systems are generally not as accurate as required and in many instances must be incorporated into the moving objects. Furthermore, adverse environmental conditions usually have deletorious effects on their performance. Accordingly, there currently exists the need for improved velocity measuring means capable of accurately detecting the velocities of moving objects from remote locations. The present invention is directed toward accomplishing this end.

SUMMARY OF THE INVENTION In accordance with the principles of the invention, the velocity of a moving object is measured by affixing an optical birefringent retardation plate to the object; determining the phase velocity differences between E and O-rays transmitted through the retardation plate at rest and in motion; and converting the phase information so obtained into linear and angular velocity measures. The apparatus comprehended by the invention comprises an optical birefringent retardation plate mounted on the moving object, a coherent light source positioned to transmit light through the retardation plate, a polarimeter positioned to receive the light thus transmitted, and a logic circuit adapted to operate on the output of the polarimeter. E- and O-ray phase velocity retardation values for the retardation plate at rest and appropriate phase velocity to linear and angular velocity conversion values are written into the logic circuit. The output of the polarimeter represents the phase velocity difference between the E- and O-rays transmitted through the moving retardation plate. The logic circuit subtracts the E- and O-ray phase velocity difference for the retardation plate at rest from this value and converts the difference into linear and angu lar velocity measures.

It is a principal object for the invention to provide a new and improved method for measuring the velocity of a moving object.

It is another principal object of the invention to provide new and improved apparatus for measuring the velocity of a moving object.

It is another object of the invention to provide highly accurate means for remotely measuring and monitoring the velocity of a moving object.

It is another object of the invention to provide means for testing the laws of composition of phase velocities.

These, together with other objects, advantages and features of the invention will become more apparent from the following detailed description when taken in conjunction with the illustrative embodiments in the accompanying drawings.

DESCRIPTION OF THE DRAWINGS ment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention is based on certain phenomena relating to the passage of light through an optical retardation plate. Optical retardation plates exhibit double refraction characteristics that cause light to be propagated in the plate material in two orthogonal directions for the electric vector. The two directions are designated as that of the E-ray (extraordinary ray) and that of the O-ray (ordinary ray). These rays travel through the material at different phase velocities, that is, the surfaces of constant phase for the E ray travels in the material at a speed different from that for the O-ray surfaces. If light is incident on a doubly refracting material perpendicular to the optic axis, the E- and O-rays which are formed in the crystal are not spatially separated as they propagate but do emerge from the crystal with a phase difference, Ad).

It has been discovered that an additional phase differ- .ence, 01, is introduced if the retardation plate is in motion relative to the light source, and further that the additional phase differences thus introduced is proportional to the velocity of the moving plate. This newly discovered phenomenon is utilized to effect the velocity measuring method and apparatus of the invention as hereinafter described. I

FIG. 1 illustrates an optical retardation plate 3 of the type comprehended by the invention. Retardation plate 3 can be fabricated of calcite or any appropriate birefringentmaterial.

The additional phase velocity difference introduced by the motion of the retardation plate and the relationship between this phase velocity difference and the velocity of the moving plate can be analytically demonstrated using Lorentz transformations for phase velocity.

The situation to be analyzed consists essentially of letting linearly polarized light fall on a moving retardation plate. In thisarrangement the light source, detector and analyzing apparatus are all stationary in the laboratory frame of reference. The only motion is that of the retardation plate.

As indicated above, the effect of the retardation plate is to divide the incident ray into an ordinary ray (0- ray) and an extraordinary ray (E-ray), each ray traveling through the plate with a characteristic phase velocity. Since these two velocities are unequal, the rays recombine on emergence from the plate with a phase difference.

Letting w and v represent the phase velocity and frequency in a stationary medium and w and v represent the transformed quantities in the medium moving with velocity v, the general transformations are v sin alw v sin a/w (I) v cos a'w v(cos a+vw/c )/w(l 1/ if the direction of propagation is in the xy plane. The angle a is the angle between the direction of propagation and the direction of velocity v as shown in FIG. 1.

If a is zero, Equations 1) reduce to v/w v(l vw/c)/w(l v /c (2 In any refractive medium the phase and ray velocities are in general different. Only if the direction of propagation is parallel to the direction of motion of the medium are the two velocities identical.

For the stationary case the difference in phase Ad) between the E-ray and O-ray on emergence from the plate is In Equation (3) T is the period, r and t, are the times required to traverse the plate for the E-ray and O-ray respectively, I is the plate thickness, and w and W are the respective phase velocities.

To calculate the corresponding quantity 13 for the moving plate is slightly more complicated. In the time t in which a ray travels through the plate, the plate itself moves a distance vt. Moreover owing to the L0- rentz contraction the plate thickness becomes [(1 v /c Therefore:

[(1 v lc v! w't 4 which, when solved for I, gives The phase difference Ad) may be written as AI P G o o The simplest case in which 0: equals zero can now be considered. By using Equations (2) the exact equation A 211 v(1 v /c {(l v/w )(l vw /c )w 1 v/ o)( 0/v ol 7 is obtained. Neglecting second or higher order terms in v/c, the following relationship is derived:

Ad) 2'rrlv l/w l/w v(l/w,, l/w

8:15 where Ad: is the stationary phase difference given by Equation (3). The additional quantity 84 arises from the motion of the plate. It can be rewritten as 54) 217' lv( l/w l/w v( l/w l/w or (9) 8d) A(n,. n v/c where n and n are the indices of refraction for the E-ray and O-ray respectively. The foregoing analysis therefore predicts an additional phase difference, first order in We and proportional to the original stationary phase difference and to the sum of the two indices.

The measurement of a phase retardation requires a polarimeter. Today it is possible to make polarimeter measurements to an accuracy of 0.01". Retardation plates themselves represent phase differences which are actually many multiples of 211'. For example, a nominal quarter wave plate has a thickness such that the retardation is 211N 17/2, where N is a large number. A slab of calcite 3 cm thick corresponds to a retardation Ad) of approximately 211- X 10 radians for 5,890A light. Hence a 8 equal to 0.l, which is 10 times greater than the limit of accuracy, would correspond to a velocity of I50 m/sec according to Equation (9). This is within experimental capabilities. Most predicted relativistic effects depend on very high velocities. The effect predicted by Equation (9) can be obtained at velocities not normally considered to be relativistic by compensating with an increased retardation Ad).

In the foregoing evaluation, the retardation plate is set into motion with respect to the source and observer, the significant velocity being the phase velocity. The analytical method used, therefore, tests the laws of composition of phase velocities. By changing the direction of motion of the plate with respect to the direction of the propagation vector the laws for all angles a can be examined.

Referring now to FIG. 2, there is illustrated thereby velocity measuring apparatus that utilizes the principles of the invention. The velocity (angular) of rotating shaft 2 is measured by mounting optical retardation plate 3 on support disc 4. Disc 4 is affixed to shaft 2. Coherent light source 5 projects light through retardation plate 3. Polarimeter 6 is positioned to receive the light so transmitted. The output of polarimeter 6 is fed to logic circuit 7. Logic circuit 7 contains the appropriate information (phase velocity to linear and angular velocity conversion factor, retardation plate and light source characteristics, etc.) required to convert the polarimeter output signal into linear and angular velocity values. Although not illustrated, arrangements for affixing the retardation plate to linearly moving objects are also within the scope of the invention.

While the invention has been described in its preferred embodiment, it is understood that the words which have been used are words of description rather than words of limitation and that changes within the purview of the appealed claims may be made without departing from the scope and spirit of the invention in its borader aspects.

I claim:

1. The method of measuring the velocity of a moving object comprising the steps of obtaining the phase velocity difference between the E- and O-rays of light transmitted through a given stationary optical birefringent retardation plate by a given stationary coherent light source, affixing said retardation plate to said moving object, projecting light through the'moving retardation plate with said stationary coherent light source,

obtaining the phase velocity difference between the E- and O-rays of the light transmitted through the moving retardation plate,

subtracting the E- and O-ray phase velocity difference obtained from the starionary retardation plate from the E and O-ray phase velocity difference obtained from the moving retardation plate, and converting the resultant value into velocity measure.

2. Apparatus for measuring the velocity of a moving object comprising an optical birefringent retardation plate affixed to the moving object,

a stationary remotely located coherent light source positioned to transmit light through said retardation plate,

means for detecting the phase velocity difference values between the E- and O-rays of the light transmitted through the moving retardation plate, and

a logic circuit connected to receive the output of said means for detecting phase velocity difference values, said logic circuit having the phase velocity difference value between the E and O-rays of coherent light transmitted through said retardation plate in a stationary condition written into its memory rays comprises a polarimeter.

UNITED STATES PATENT ormtr CERTIFICATE OF Patent; No. 3,791,73 Dated February 12, 197A Inventor(s) Ronald G. Newburgh It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

On front page, after Data Element Identifier [19],

change "Newburg; to Newburgh On front page, after Data Element Identifier [75],

Signed and sealed this 5th day of November 1974..

change "Ronald G. Newbur g" to Ronald Gt. Newbur'gh (SEAL) Attost:

MCCOY M. GIBSON JR. C. MARSHALL DANN Attesting Officer Commissioner of Patents FORM Po-wso (10-69) UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No, 3,79 ,73 Dated February 12, 1974 Inventor) Ronald G. Newbur'gh It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

On front page, after Data Element Identifier- [19],

change "Newburg" to Newburgh On front page, after- Data Element Identifier [75],

change "Ronald G. Newburg" to Ronald G.v Newburgh Signed and sealed this 5th day of November 1974.

(SEAL) Attest:

MCCOY M. GIBSON JR. C. MARSHALL DANN Attesting Officer Commissioner of Patents FORM PC4050 (1069) J. USCOMM-DC 603704 69 U.$ GOVERNMENT PRINTING OFFICE: II" 0-3'6-334. 

1. The method of measuring the velocity of a moving object comprising the steps of obtaining the phase velocity difference between the E- and Orays of light transmitted through a given stationary optical birefringent retardation plate by a given stationary coherent light source, affixing said retardation plate to said moving object, projecting light through the moving retardation plate with said stationary coherent light source, obtaining the phase velocity difference between the E- and Orays of the light transmitted through the moving retardation plate, subtracting the E- and O-ray phase velocity difference obtained from the starionary retardation plate from the E and O-ray phase velocity difference obtained from the moving retardation plate, and converting the resultant value into velocity measure.
 2. Apparatus for measuring the velocity of a moving object comprising an optical birefringent retardation plate affixed to the moving object, a stationary remotely located coherent light source positioned to transmit light through said retardation plate, means for detecting the phase velocity difference values between the E- and O-rays of the light transmitted through the moving retardation plate, and a logic circuit connected to receive the output of said means for detecting phase velocity difference values, said logic circuit having the phase velocity difference value between the E- and O-rays of coherent light transmitted through said retardation plate in a stationary condition written into its memory circuits, Said logic circuit being adapted to convert the phase velocity difference value stored in its memory circuits and the phase velocity difference values received from said means for detecting the phase velocity difference values into linear and angular velocity values.
 3. Apparatus for measuring the velocity of a moving object as defined in claim 2 wherein said optical birefringent retardation plate comprises a calcite crystal plate.
 4. Apparatus for measuring the velocity of a moving object as defined in claim 3 wherein said means for detecting phase velocity difference between E- and O-rays comprises a polarimeter. 